The Argentine, returning to the San Paolo stadium for the second time since his acrimonious exit last year and booed throughout, did not celebrate his goals which gave Juve a 5-4 aggregate win over Napoli in the two-legged semi-final.
The holders appeared to be cruising as they led 2-1 on the hour but two quick Napoli goals, the first following a howler from Juve goalkeeper Neto, forced them to resort to time-wasting and gamesmanship in the last 20 minutes.
Juve, who will face Lazio in the final, stayed on course for a possible treble as they lead Serie A by six points and have reached the Champions League quarter-finals.
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By a quirk in the fixture list, it was the teams' second meeting in four days at the San Paolo following Sunday's 1-1 draw in Serie A which Napoli dominated.
Higuain, previously a hero with Napoli fans until Juventus triggered a buyout clause in his contract and signed the striker in July, made little impact then but was not so subdued second time around.
Juve, featuring seven South Americans in their starting lineup, brought a 3-1 lead from the first leg and Higuain gave them a precious away goal when he was given time and space to turn and fire a bouncing shot past Pepe Reina from outside the area in the 32nd minute.
Marek Hamsik, who scored in Sunday's match, levelled in the 53rd minute only for Higuain to put Juve back in front six minutes later when he turned in Juan Cuadrado's cross.
Napoli were left needing four goals and quickly got two of them.
Neto, who stands in for veteran Gianluigi Buffon in Coppa Italia games, tried to control a throw-in with his feet but missed the ball and Dries Mertens scored into an open goal barely 20 seconds after coming on as a substitute.
Jose Callejon then set up another for Lorenzo Insigne in the 67th minute with some neat footwork but Juventus managed to disrupt Napoli's rhythm with spoiling tactics.
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